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MathGroup Archive 2005

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Re: Nonlinear Curve Fitting

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53839] Re: [mg53812] Nonlinear Curve Fitting
  • From: DrBob <drbob at bigfoot.com>
  • Date: Sat, 29 Jan 2005 06:02:47 -0500 (EST)
  • References: <200501280743.CAA00362@smc.vnet.net>
  • Reply-to: drbob at bigfoot.com
  • Sender: owner-wri-mathgroup at wolfram.com

For reasonable values of a and b, the proposed fit function can be real-valued only if c > x, so we need to restrict c to something greater than the largest x value.

Define:

data=(your data here)

Clear[y]
c = Max[data[[All,1]]] + E^d;
y[x_, a_, b_, d_] = a*(1 - x/c)^b;

and solve this way (NonlinearFit could be used instead of NonlinearRegress):

<< Statistics`NonlinearFit`
Off[NonlinearRegress::"crvtab"]
BestFitParameters /. NonlinearRegress[data, y[x, a, b, d], x, {a, b, d}]
{a, b, c} /. %
yFit[x_] = y[x, a, b, d] /. %%

{a -> 0.318854, b -> 0.204693, d -> 0.724684}
{0.318854,0.204693,384.614}
0.3188541114916767*(1 - 0.0026000088278186092*x)^0.20469343211850052

{min, max} = Through[{Min, Max}@data[[All, 1]]];
DisplayTogether[Plot[yFit@x, {x, min, max}], ListPlot@data]

Bobby

On Fri, 28 Jan 2005 02:43:59 -0500 (EST), nilaakash <nilaakash at gmail.com> wrote:

> Dear Friends,
>               I have tried to fit a nonlinear curve, but failed. I am
> giving my points and it's curve equation is
>
>     \!\(y = a \((1 - x\/c)\)\^b\)
>
> Here a, b, c are fit parameters. My initial guess is like
>    a =   0.3
>    b =   0.2
>    c = 385.2
>
> data={{382.55, 0.112531}, {382.351, 0.113271}, {382.15, 0.115013},
> {381.95,
>     0.116646}, {381.749, 0.118108}, {381.549, 0.119477}, {381.352,
>     0.120815}, {381.15, 0.122088}, {380.95, 0.123275}, {380.75,
>     0.124776}, {380.55, 0.125688}, {380.35, 0.126676}, {380.15,
>     0.127719}, {379.95, 0.128744}, {379.75, 0.129687}, {379.549,
>     0.130706}, {379.35, 0.131595}, {379.149, 0.132522}, {378.95,
>     0.133465}, {378.75, 0.134297}, {378.55, 0.135198}, {378.35,
>     0.135965}, {378.15, 0.136919}, {377.95, 0.137599}, {377.749,
>     0.138507}, {377.55, 0.139172}, {377.35, 0.140088}, {377.15,
>     0.140695}, {376.95, 0.141593}, {376.75, 0.142154}, {376.55,
>     0.143089}, {376.35, 0.143644}, {376.149, 0.144522}, {375.95,
>     0.14509}, {375.75, 0.145836}, {375.55, 0.14655}, {375.35,
>     0.147098}, {375.15, 0.147927}, {374.95, 0.148362}, {374.749,
>     0.149214}, {374.55, 0.149868}, {374.35, 0.150402}, {374.15,
>     0.151099}, {373.949, 0.151528}, {373.75, 0.1524}, {373.55,
>     0.152919}, {373.35, 0.153435}, {373.15, 0.154261}, {372.95,
>     0.154473}, {372.75, 0.155232}, {372.55, 0.155874}, {372.35,
>     0.156397}, {372.149, 0.156851}, {371.949, 0.157775}, {371.75,
>     0.158082}, {371.55, 0.158616}, {371.349, 0.15936}, {371.15,
>     0.159811}, {370.95, 0.160188}, {370.75, 0.161122}, {370.55,
>     0.16138}, {370.35, 0.161574}, {370.15, 0.162232}, {369.949,
>     0.163392}, {369.751, 0.163124}, {369.55, 0.163277}, {369.35,
>     0.164757}, {369.15, 0.164471}, {368.95, 0.164512}, {368.75,
>     0.165126}, {368.55, 0.166819}, {368.35, 0.168995}, {368.15,
>     0.168555}, {367.95, 0.168609}, {367.75, 0.169652}, {367.55,
>     0.169828}, {367.35, 0.169679}, {367.15, 0.169972}, {366.95,
>     0.170693}, {366.751, 0.171106}, {366.55, 0.171399}, {366.35,
>     0.171651}, {366.15, 0.172006}, {365.95, 0.172645}, {365.75,
>     0.173137}, {365.55, 0.173136}, {365.35, 0.173773}, {365.15,
>     0.174123}, {364.95, 0.174443}, {364.75, 0.174802}, {364.55,
>     0.175113}, {364.35, 0.175806}, {364.15, 0.176169}, {363.95,
>     0.176401}, {363.75, 0.176578}, {363.55, 0.176953}, {363.35,
>     0.177432}, {363.15, 0.177765}, {362.95, 0.177845}, {362.75,
>     0.178067}, {362.55, 0.178569}, {362.35, 0.179083}, {362.15,
>     0.179272}, {361.95, 0.179384}, {361.75, 0.179777}, {361.551,
>     0.180256}, {361.349, 0.180579}, {361.15, 0.180718}, {360.95,
>     0.181023}, {360.75, 0.18146}, {360.55, 0.181936}, {360.35,
>     0.181999}, {360.151, 0.182136}, {359.95, 0.182558}, {359.75,
>     0.183018}, {359.55, 0.183377}, {359.35, 0.183487}, {359.15,
>     0.183709}, {358.95, 0.184118}, {358.75, 0.184511}, {358.55,
>     0.184856}, {358.35, 0.184902}, {358.15, 0.185134}, {357.95,
>     0.18549}, {357.75, 0.185944}, {357.55, 0.186194}, {357.35,
>     0.186338}, {357.15, 0.186497}, {356.95, 0.186801}, {356.75,
>     0.187286}, {356.55, 0.187679}, {356.35, 0.187856}, {356.15,
>     0.187953}, {355.95, 0.188292}, {355.75, 0.188656}, {355.55,
>     0.189001}, {355.35, 0.189234}, {355.15, 0.189379}, {354.95,
>     0.189551}, {354.75, 0.189823}, {354.549, 0.190173}, {354.35,
>     0.190491}, {354.15, 0.19072}, {353.95, 0.190911}, {353.75,
>     0.191116}, {353.55, 0.19133}, {353.35, 0.191617}, {353.15,
>     0.191903}, {352.95, 0.192179}, {352.75, 0.192324}, {352.55,
>     0.192525}, {352.35, 0.192726}, {352.15, 0.193037}, {351.95,
>     0.193273}, {351.75, 0.193512}, {351.55, 0.193766}, {351.35,
>     0.193925}, {351.151, 0.194099}, {350.95, 0.194293}, {350.75,
>     0.194514}, {350.55, 0.194769}, {350.35, 0.195005}, {350.15,
>     0.19527}, {349.95, 0.195444}, {349.75, 0.195603}, {349.55,
>     0.195743}, {349.35, 0.195977}, {349.15, 0.196241}, {348.95,
>     0.196497}, {348.75, 0.196661}, {348.55, 0.196848}, {348.35,
>     0.197031}, {348.15, 0.197189}, {347.95, 0.197359}, {347.75,
>     0.197566}, {347.55, 0.197798}, {347.35, 0.198015}, {347.15,
>     0.198241}, {346.95, 0.198459}, {346.75, 0.198643}, {346.55,
>     0.198803}, {346.35, 0.198968}, {346.15, 0.199108}, {345.95,
>     0.199294}, {345.75, 0.199527}, {345.55, 0.199761}, {345.35,
>     0.200008}, {345.15, 0.200202}, {344.95, 0.200311}, {344.75,
>     0.200481}, {344.55, 0.20064}, {344.35, 0.200819}, {344.15,
>     0.201037}, {343.95, 0.201279}, {343.75, 0.201518}, {343.551,
>     0.201718}, {343.35, 0.201888}, {343.15, 0.202039}, {342.95,
>     0.20219}, {342.75, 0.202339}, {342.55, 0.202529}, {342.35,
>     0.202706}, {342.15, 0.202881}, {341.95, 0.203091}, {341.75,
>     0.203274}, {341.55, 0.203498}, {341.35, 0.203684}, {341.15,
>     0.203875}, {340.95, 0.204088}, {340.75, 0.204272}, {340.55,
>     0.204489}, {340.35, 0.204658}, {340.15, 0.204811}, {339.95,
>     0.20495}, {339.75, 0.205069}, {339.55, 0.205247}, {339.35,
>     0.205441}, {339.15, 0.20562}, {338.95, 0.205837}, {338.75,
>     0.206019}, {338.55, 0.206215}, {338.35, 0.206369}, {338.15,
>     0.206536}, {337.95, 0.206684}, {337.75, 0.206844}, {337.55,
>     0.206981}, {337.35, 0.207116}, {337.15, 0.207285}, {336.95,
>     0.207474}, {336.75, 0.207668}, {336.55, 0.207867}, {336.35,
>     0.208033}, {336.15, 0.208205}, {335.95, 0.20837}, {335.75,
>     0.208516}, {335.552, 0.208639}, {335.35, 0.208779}, {335.15,
>     0.208952}, {334.95, 0.209164}, {334.75, 0.209378}, {334.55,
>     0.209519}, {334.35, 0.209637}, {334.15, 0.209792}, {333.95,
>     0.209865}, {333.75, 0.210065}, {333.55, 0.210288}, {333.35,
>     0.210415}, {333.15, 0.210534}, {332.95, 0.210705}, {332.75,
>     0.210876}, {332.55, 0.211065}, {332.35, 0.211264}, {332.15,
>     0.211427}, {331.95, 0.211577}, {331.75, 0.211715}, {331.55,
>     0.211856}, {331.35, 0.212039}, {331.15, 0.212206}, {330.949,
>     0.212384}, {330.75, 0.212548}, {330.55, 0.212727}, {330.35,
>     0.212883}, {330.15, 0.213023}, {329.95, 0.213175}, {329.75,
>     0.21334}, {329.55, 0.213508}, {329.35, 0.213678}, {329.15,
>     0.21385}, {328.95, 0.213997}, {328.75, 0.214134}, {328.55,
>     0.21429}, {328.35, 0.214471}, {328.15, 0.214574}, {327.95,
>     0.214685}, {327.75, 0.214832}, {327.55, 0.214982}, {327.35,
>     0.215121}, {327.15, 0.215276}, {326.949, 0.215443}, {326.75,
> 0.215625}}
>
> Please help me to find out best a, b, c fit parameters.
>
> Thanks.
>
> nilaakash
>
>
>
>



-- 
DrBob at bigfoot.com
www.eclecticdreams.net


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